Question

Jobs arrive at the server at the rate of 8 jobs per hour. The service takes 3 minutes, on the average. This system is modeled by the Bernoulli single-server queuing process with 5-second frames and capacity limited by 3 jobs. Write the transition probability matrix for the number of jobs in the system at the end of each frame.

Answer 1

2249 / 540000

Explanation:

Jobs arrival time = 8 jobs per hour

Service takes 3 minutes on average

Frame size = 5 second

capacity of each frame = 3 jobs

Determine the transition probability matrix for number of jobs in system

First step : find probability of job arrival

= 8 / ( 5 * 3600)

= 8 / 18000 = 1 / 2250

next : determine probability of service

= ( 3 * 5 )/ 3600

= 15 / 3600 = 1/240

Finally the transition probability matrix ( p10 )= { 1, 0}

= probability of service(1 - probability of arrival)

= 1/ 240 * ( 1 - 1 / 2250 )

= 1 / 240 * ( 2249 / 2250 )

= 2249 / 540000